How can interfaces replace the need for multiple inheritance when have existing classes

Actually, I have no good answer other than Java SHOULD have Multiple Inheritance. The whole point that interfaces should be able to replace the need for Multiple Inheritance is like the big lie that when repeated enough times becomes true.

The argument is that Multiple Inheritance causes all these problems (la-di-dah), yet I keep hearing those arguments from Java developers who have never used C++. I also don't EVER remember C++ programmers saying "Gee, I love C++, but if they would only get rid of Multiple Inheritance, it would become a great language". People used it when it was practical and didn't when it wasn't.

Your problem is a classic case of where Multiple Inheritance would be appropriate. Any suggestion to refactor the code is really telling you how to work around the PROBLEM that Java has no Multiple Inheritance.

Also all the discussion that "oh, delegation is better, la-di-dah" is confusing religion with design. There is no right way. Things are either more useful or less useful and that is all.

In your case Multiple Inheritance would be more useful and a more elegant solution.

As far as refactoring your code into a less useful form to satisfy all the religious people who have never used Multiple Inheritance and believe "Multiple Inheritance is bad", I guess you will have to downgrade your code because I don't see Java "improving" in that way any time soon. There are too many people repeating the religious mantra to the point of stupidity that I can't see it ever being added to the language.

Actually, my solution for you would be "x extends Tagged, XMLElement" and that would be all.

...but as you can see from the solutions provided above, most people think that such a solution would be WAY TOO COMPLEX AND CONFUSING!

I would prefer to venture into the "x extends a,b" territory myself, even if it is a very frightening solution that might overwhelm the abilities of most Java programmers.

What is even more amazing about the solutions suggested above is that everyone here who suggested that you refactor your code into "delegation" because Multiple Inheritance is bad, would, if they were confronted with the very same problem, would solve the problem by simply doing: "x extends a,b" and be done with it, and all their religious arguments about "delegation vs inheritance" would disappear. The whole debate is stupid, and it only being advanced by clueless programmers who only demonstrate how well they can recite out of a book and how little they can think for themselves.

You are 100% correct that Multiple Inheritance would help, and no, you are doing anything wrong in your code if you think Java should have it.

You should probably favor composition (and delegation) over inheritance :

public interface TaggedInterface {
    void foo();
}

public interface XMLElementInterface {
    void bar();
}

public class Tagged implements TaggedInterface {
    // ...
}

public class XMLElement implements XMLElementInterface {
    // ...
}

public class TaggedXmlElement implements TaggedInterface, XMLElementInterface {
    private TaggedInterface tagged;
    private XMLElementInterface xmlElement;

    public TaggedXmlElement(TaggedInterface tagged, XMLElementInterface xmlElement) {
        this.tagged = tagged;
        this.xmlElement = xmlElement;
    }

    public void foo() {
        this.tagged.foo();
    }

    public void bar() {
        this.xmlElement.bar();
    }

    public static void main(String[] args) {
        TaggedXmlElement t = new TaggedXmlElement(new Tagged(), new XMLElement());
        t.foo();
        t.bar();
    }
}

Similar to what Andreas_D suggested but with the use of inner classes. This way you indeed extend each class and can override it in your own code if desired.

interface IBird {
    public void layEgg();
}

interface IMammal {
    public void giveMilk();
}

class Bird implements IBird {
    public void layEgg() {
        System.out.println("Laying eggs...");
    }
}

class Mammal implements IMammal {
    public void giveMilk() {
        System.out.println("Giving milk...");
    }
}

class Platypus implements IMammal, IBird {

    private class LayingEggAnimal extends Bird {}
    private class GivingMilkAnimal extends Mammal {}

    private LayingEggAnimal layingEggAnimal = new LayingEggAnimal();

    private GivingMilkAnimal givingMilkAnimal = new GivingMilkAnimal();

    @Override
    public void layEgg() {
        layingEggAnimal.layEgg();
    }

    @Override
    public void giveMilk() {
        givingMilkAnimal.giveMilk();
    }
}